Block #685,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/20/2014, 1:06:17 PM · Difficulty 10.9560 · 6,124,219 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

e808b2b2a445cb0416fbefbb9c5e5cb53033dddd579bd422fc9eb3c6b0f7fa02

View on Chainz ↗

Height

#685,112

Difficulty

10.956048

Transactions

Size

658 B

Version

Bits

0af4bf95

Nonce

785,222,883

Timestamp

8/20/2014, 1:06:17 PM

Confirmations

6,124,219

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6848296882fc4ae9a03b6bdb7dc1c96cd2f44efbf6475e7584be4f540da88033

Transactions (3)

Coinbasea8da5ca8c7d50f…c4502eb9a9da0f

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

7be3cc4abf66a9…065916eaf28074

1 in → 3 out8.3100 XPM225 B

AeKNrjNj…1NEq95Ta AH1wEe2R…srAfPtHd ALeH3dPN…zVgWRzZU

ba9bf3bdd8f9b1…2d664154eabd83

1 in → 2 out3.1314 XPM226 B

ARSrvv1x…ZaaviNgn AH9SN9C3…7id3Rssh

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.016 × 10⁹⁶(97-digit number)

10165490268321660049…87820985684327001599

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.016 × 10⁹⁶(97-digit number)

10165490268321660049…87820985684327001599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.016 × 10⁹⁶(97-digit number)

10165490268321660049…87820985684327001601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.033 × 10⁹⁶(97-digit number)

20330980536643320098…75641971368654003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.033 × 10⁹⁶(97-digit number)

20330980536643320098…75641971368654003201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.066 × 10⁹⁶(97-digit number)

40661961073286640196…51283942737308006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.066 × 10⁹⁶(97-digit number)

40661961073286640196…51283942737308006401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

8.132 × 10⁹⁶(97-digit number)

81323922146573280393…02567885474616012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.132 × 10⁹⁶(97-digit number)

81323922146573280393…02567885474616012801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.626 × 10⁹⁷(98-digit number)

16264784429314656078…05135770949232025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.626 × 10⁹⁷(98-digit number)

16264784429314656078…05135770949232025601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #685,112

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